Dynamic Control Law Research Articles

Decentralized Robust Tracking Control of Interconnected Nonlinear‐Constrained Systems: A Dynamic Event‐Sampled Method

ABSTRACTThis paper presents a decentralized robust dynamic event‐sampled tracking (EST) control law for interconnected nonlinear‐constrained systems. The core of developing such a control law is to convert the original EST control problem into the event‐sampled decentralized stabilization problem of augmented interconnected systems. To address the transformed decentralized stabilization problem, an indirect approach relying on the optimal control methodology is proposed. Initially, a group of cost functions are constructed for the nominal subsystems related to the augmented interconnected systems. Then, the dynamic event‐sampling mechanisms are introduced for lessening the computational burden. Meanwhile, the event‐sampled Hamilton–Jacobi–Bellman equations (ES‐HJBEs) are proposed for the augmented interconnected systems. To approximately solve the ES‐HJBEs, the critic approximators are used with their parameters tuned under the reinforcement learning framework. After that, the uniform ultimate boundedness of the tracking errors and the approximators' parameter estimation errors are assured based on the Lyapunov theorem. Finally, a nonlinear plant is provided to validate the decentralized robust dynamic EST control law.

Position and reduced attitude trajectory tracking control of quadrotors: Theory and experiments

Multirotor aerial vehicles are versatile flying robots that perform hovering, vertical take-off and landing, and aggressive maneuvers in a 3D environment. Due to their underactuated nature, the aerial vehicles' position and orientation cannot be controlled independently. For this reason, most of the quadrotors' tasks involved position tracking or regulation tasks. This paper focuses on the position-tracking problem of quadrotors using the reduced orientation of the vehicle, meaning that only two degrees of freedom of the robot's orientation are controlled. We propose an almost global exponential reduced attitude control law that aligns the aerial robot's thrust direction with the desired force that drives the robot along the desired position trajectory. For the translational subsystem, we propose a dynamic control law that drives the position and velocity of the quadrotors asymptotically to the desired trajectories. The proposed attitude control law is computationally simple, and thus, it is suitable to run on board. Finally, we provide experimental results performed on a low-cost quadrotor and a comparison study with a full-attitude controller to illustrate the performance and advantages of the proposed control laws.

Image-Based Visual Servoing of Manipulators With Unknown Depth: A Recurrent Neural Network Approach.

The image-based visual servoing (IBVS) of manipulators is important for intelligent manipulation using visual feedbacks. While the traditional IBVS methods for manipulators require the knowledge of the depth information in the interaction matrix, in this article, we propose a novel IBVS method for manipulators without depth estimation by leveraging the property of the associated image Jacobian. Because of a novel transformation, the IBVS problem is converted into a convex optimization problem subject to the kinematic constraint, joint constraints, and other constraints that are not explicitly related to the depth information. The problem is then solved by developing a recurrent neural network of global asymptotic convergence, and a dynamic neural control law without depth estimation emerges for the IBVS of manipulators. The theoretical guarantee and simulation results are provided to show the efficacy of the proposed method.

Dynamic event-triggered neuro-optimal control for uncertain nonlinear systems with unknown dead-zone constraint

In this article, we propose a dynamic event-triggered neuro-optimal control scheme (DETNOC) for uncertain nonlinear systems subject to unknown dead-zone and disturbances through the design of a composite control law. An integral sliding mode-based discontinuous control law is utilized to compensate for the effects of unknown dead-zone, disturbance, and a component of uncertainties. As a result, a system dynamics that evolves free of these effects during the sliding mode is obtained. Then, an adaptive dynamic programming-based dynamic event-triggered optimal control law is designed to stabilize the sliding mode dynamics with the help of critic-only neural network architecture. Finally, stability analysis of the closed-loop system is provided and the effectiveness of the developed DETNOC scheme is verified.

Aerodynamic Feedforward-Feedback Architecture for Tailsitter Control in Hybrid Flight Regimes

This paper presents a guidance-control design methodology for the autonomous maneuvering of tailsitter transitioning unmanned aerial systems (t-UASs) in hybrid flight regimes (i.e., the dynamics between VTOL and fixed-wing regimes). The tailsitter guidance-control architecture consists of a trajectory planner, an outer-loop position controller, an inner-loop attitude controller, and a control allocator. The trajectory planner uses a simplified tailsitter model, with aerodynamic and wake effect considerations, to generate a set of transition trajectories with associated aerodynamic force estimates based on an optimization metric specified by a human operator (minimum time transition). The outer-loop controller then uses the aerodynamic force estimate computed by the trajectory planner as a feedforward signal alongside feedback linearization of the outer-loop dynamics for 6DOF position control. The inner-loop attitude controller is a standard nonlinear dynamic inversion control law that generates the desired pitch, roll, and yaw moments, which are then converted to the appropriate rotor speeds by the control allocator. Analytical conditions for robust stability are derived for the outer-loop position controller to guarantee performance in the presence of uncertainty in the feedforward aerodynamic force compensation. Finally, both tracking performance and stability of the control architecture are evaluated on a high-fidelity flight dynamics simulation of a quadrotor biplane tailsitter for flight missions that demand high maneuverability in transition between flight modes.

Dynamic event-triggered synchronization for semi-Markovian switching inertial neural networks with generally uncertain transition rates in finite-time interval

This paper investigates the finite-time synchronization for inertial neural networks with stochastic switching parameters based on dynamic event-triggered protocol. Due to the complexity of network environment, semi-Markovian process is introduced into the modeling of inertial neural networks, in which the transition rates vary with the operating time. The dynamic event-triggered protocol is developed to determine whether the signal is transmitted, in which Zeno phenomenon is eliminated under limited bandwidth resources. The objective is to construct an appropriate dynamic event-triggered control law such that the drive-response system maintains finite-time synchronization under generally uncertain transition rates. Based on the Lyapunov functional theory, finite-time synchronization criterion is proposed for the related inertial neural networks. Furthermore, a dynamic event-triggered controller is constructed in a finite-time interval. A numerical example and an image encryption process are given to show the efficiency of the proposed method.

Nonlinear control of coaxial double rotor magnetic gear based on high gain observer in wind turbine

AbstractThis paper proposes a nonlinear control law with a dynamic controller based on high gain observer (HGO) for a co‐axial double rotor magnetic gear (CADRMG) based on Halbach array used in wind turbines. The generalized canonical form (GCF) is used to normalize the nonlinear augmented system to achieve the dynamic control signal with a chain of integrator of system output. In addition, a tracking problem is defined to track high speed rotor (HSR) with respect to GCF. On the other hand, the HGO is used to estimate the error tracking at the expense of nonlinear terms. Furthermore, the nonlinear system observability of the augmented system is evaluated. A dynamic control law is used to solve the tracking problem based on HGO. This controller can eliminate the effect of load torque as a constant and unknown disturbance in the closed‐loop system. Moreover, the closed‐loop stability of the system under dynamic signal control is guaranteed. The system states estimation is calculated by recursive equations from tracking error estimations. Finally, numerical simulations are given to illustrate the theoretical results of proposed system.

Nearly optimal stabilization of unknown continuous-time nonlinear systems: A new parallel control approach

This paper develops a novel online nearly optimal control (ONOC) method for unknown continuous-time (CT) nonaffine nonlinear systems without recovering unknown systems. First, a dynamic control law is proposed for CT nonaffine nonlinear systems using parallel control. To achieve the proposed dynamic control law, an affine augmented system (AAS) is constructed according to the original system, and an augmented performance index (API) is constructed on the basis of the original performance index (OPI). Then, the stability relationship between the original system and the AAS is provided, and it is proven that, by selecting a suitable parameter in the API, optimal control of the AAS with the API is equivalent to near-optimal control of the original system with the OPI. Subsequently, based on the proposed dynamic control law, we extend integral reinforcement learning (IRL) to completely unknown CT nonaffine systems, and it is further proved that closed-loop signals are uniformly ultimately bounded (UUB) without the assumption that the input dynamics are bounded. Furthermore, the OPI can be set to an arbitrary positive-definite form, and the UUB bound for the state vector can be predetermined. Lastly, simulations are offered to exhibit the correctness of the developed ONOC method. Source code of this paper is available at: https://github.com/lujingweihh/Adaptive-dynamic-programming-algorithms/tree/main/model_free_integral_reinforcement_learning.

Solutions to the output regulation problem of time-varying descriptor systems

This paper studies the output regulation problem of time-varying descriptor systems and the problem of designing state feedback and dynamic measurement output feedback control laws which asymptotically achieves output regulation and disturbance rejection is considered. New regulator equations are proposed for time-varying descriptor systems in the form of differential-algebraic matrix equations. The unique solution of the proposed regulator equations is given as well. We prove that the output regulation problem of time-varying descriptor systems is solvable if and only if the given regulator equations are solvable. Based on the solution of the regulator equations, the state feedback and dynamic measurement output feedback control laws are designed to solve the output regulation problem. The work extends the existing results of output regulation problem for time-varying linear systems to the time-varying descriptor systems. Numerical examples are given to show the effectiveness of our methodology.

Output regulation and tracking for linear ODE-hyperbolic PDE–ODE systems

This paper proposes a constructive solution to the output regulation — output tracking problem for a general class of interconnected systems. The class of systems under consideration consists of a linear 2 × 2 hyperbolic Partial Differential Equations (PDE) system coupled at both ends with Ordinary Differential Equations (ODEs). The proximal ODE system, which represents actuator dynamics, is actuated. Colocated measurements are available. The distal ODE system represents the load dynamics. The control objective is to ensure, in the presence of a disturbance signal (regulation problem), that a virtual output exponentially converges to zero. By doing so, we can ensure that a state component of the distal ODE state robustly converges towards a known reference trajectory (output tracking problem) even in the presence of a disturbance with a known structure. The proposed approach combines the backstepping methodology and frequency analysis techniques. We first map the original system to a simpler target system using an invertible integral change of coordinates. From there, we design an adequate full-state feedback controller in the frequency domain. Following a similar approach, we propose a state observer that estimates the state and reconstructs the disturbance from the available measurement. Combining the full-state feedback controller with the state estimation results in a dynamic output-feedback control law. Finally, existing filtering techniques guarantee the closed-loop system robustness properties.

Sliding-mode control for heterogeneous vehicular platoons with unknown matched and mismatched disturbances under intermittent communications

In this work, we investigate a longitudinal platooning control problem of heterogeneous vehicles with a focus on external unknown disturbances, parameter uncertainties and intermittent communications. When vehicle platooning encounter intermittent communications, the performance of the platooning will be degraded. Nevertheless, the existing researches can not deal with the aforementioned three issues effectively. To this end, a novel nonsingular dynamic terminal sliding-mode control (NDTSMC) law is contrived. First, for a heterogeneous cooperative adaptive cruise control (CACC) or adaptive cruise control (ACC) platooning system of mixed vehicles, a hybrid mathematical reference model is developed. Then, we propose a CACC-ACC switched approach which activates either a CACC mode or an enhanced ACC mode relied on communication reliability. The unknown disturbances and parameter uncertainties can be together served as a unknown lumped matched (or mismatched) disturbance, depending on the circumstances. The unknown lumped matched (or mismatched) disturbance can be estimated by a finite-time disturbance observer (FTDO). Based on the observation, a novel switched controller consisting of a baseline controller part and an observation-based NDTSMC law part is proposed. Furthermore, combined with Lyapunov stability theory, it can be demonstrated that the stability of the string of mixed vehicles in the heterogeneous platoon can be robustly guaranteed after switching. Simulation examples show that the proposed approach exhibits satisfactory control properties for addressing intermittent communications. The convincing performances for attenuating parameter uncertainties and external unknown disturbances are achieved, which are also shown in simulations.

Aperiodic dynamic event-triggered control for linear systems: A looped-functional approach

The recent literature on event-triggered control has demonstrated the potential of dynamic periodic event-triggered control. Compared to continuous-time event-triggering rules, the benefit of considering periodic event-triggered control is to avoid the Zeno phenomenon, which refers to the situation when there are an infinite number of updates in a bounded interval of time. The idea of periodic event-triggered control is to trigger the control law only at known allowable periodic sampling instants. In this paper, our objective is to relax the constraint on the periodicity of the allowable sampling instants and to adapt this framework to the dynamic event-triggered control, which has not been considered in the literature, as far as we are aware of. Following the successful efforts to assess the stability of aperiodic sampled-data control, here we propose a generic framework to emulate aperiodic dynamic event-triggered control law for linear systems, for which the allowable sampling instants are not necessarily equidistant. Such an analysis is made possible thanks to the looped-functionals framework, which gives the flexibility to consider the periodic/aperiodic static/dynamic event-triggered control in a single formulation. Finally, the efficiency of the proposed results is illustrated through the study of two academic examples.

Robust Output Regulation of Linear Uncertain Systems by Dynamic Event-Triggered Output Feedback Control.

In this article, the robust output regulation problem of the linear uncertain system is investigated by the event-triggered control approach. Recently, the same problem is addressed by an event-triggered control law where the Zeno behavior may happen when time tends to infinity. In comparison, a class of event-triggered control laws is developed to achieve output regulation exactly, and meanwhile, explicitly exclude the Zeno behavior for all time. In particular, a dynamic triggering mechanism is first developed by introducing a dynamic changing variable with specific dynamics. Then, by the internal model principle, a class of dynamic output feedback control laws is designed. Later, a rigorous proof is provided to show that the tracking error of the system converges to zero asymptotically while prohibiting the Zeno behavior for all time. Finally, we give an example to illustrate our control approach.

Dynamic Output Feedback-Based Tracking Control Design With Input Time-Varying Delay for Fuzzy Systems

The prime purpose of this study is to design an output tracking control law in the perspective of compensating the effects induced by time-varying input delays and disturbances. In particular, the control protocol is developed for nonlinear systems, where the nonlinearities are effectively represented as a convex summation of linear subsystems using membership functions, which is precisely referred by fuzzy model approach. Accordingly, with the aid of parallel distributed compensation strategy and extended Smith predictor approach, the fuzzy-dependent dynamic control law is formulated. Moreover, the improved-equivalent-input-disturbance estimator approach is implemented to estimate the disturbance signals, whose output are tied to the resultant dynamic output feedback controller. On such circumstances, the controller gain matrices that assures the asymptotic tracking performance of the addressed system is calculated by solving the derived set of sufficient conditions. Conclusively, the effectiveness of the developed theoretical outcomes is validated by virtue of numerical simulations.

Asynchronous sampled-data dynamic output feedback control for Markovian jump neural networks via a double-mode-dependent Lyapunov functional

This paper discusses the asynchronous switching problem of Markovian jump neural networks (MJNNs) with mode-dependent time delays. Due to the factors such as communication induced phenomena or the incomplete availability of system modes, asynchronous switching between the system mode and the controller mode is a common phenomenon. Therefore considering the mode mismatch phenomenon and the incomplete measurement of system state, we propose an asynchronous dynamic output feedback control (DOFC) law. Unlike the traditional DOFC, the sampled-data strategy is introduced into DOFC to alleviate the burden of the communication network. In light of the sampled-data DOFC, an augmented dynamic system is modeled. To fully employ the mode information of asynchronous switching and to relax the conservativeness of the results, a double-mode-dependent Lyapunov functional is constructed, which depends both on the system modes and the DOFC modes. Then, a less conservative stability condition is obtained to guarantee mean-square asymptotic stability (MSAS) of the augmented system. On the basis of the stability condition, a design algorithm is attained to solve the gain matrices of the asynchronous DOFC. Finally, a simulation example is given to illustrate the validity and superiority of the developed results.

Finite-Time Adaptive Dynamic Surface Asymptotic Tracking Control of Uncertain Multi-Agent Systems with Unknown Control Gains

In this work, the finite-time asymptotic tracking control problem of uncertain multi-agent systems with unknown control gains is studied. For the unknown control gain of each subsystem in multi-agent systems, we consider using the Nussbaum gain function techniques to handle them. To deal with the unknown uncertain nonlinear dynamics, the radial basis function neural network is introduced in each step of the dynamic surface control design. In addition, a nonlinear compensating term with the estimation of an unknown bounded parameter is designed to avoid repeated differentiation of each virtual control law. Then, based on the neural network control method, dynamic surface control technique, and finite-time control theory, an adaptive neural network finite-time dynamic surface control law is finally designed. Using stability analysis, it is proven that the presented adaptive control law can guarantee all signals of the closed-loop system semi-global practical finite-time stable, and the tracking error of each follower agent can converge to a small neighborhood of zero in finite time. Finally, a class of single-link robot systems is provided to illustrate the effectiveness of the designed control law.

Research on Lateral Maneuverability of a Supercavitating Vehicle Based on RBFNN Adaptive Sliding Mode Control with Rolling Restriction and Planing Force Avoidance

This paper addresses the lateral motion control of a supercavitating vehicle and studies its ability to maneuver. According to the unique hydrodynamic characteristics of the supercavitating vehicle, highly coupled nonlinear 6-degree-of-freedom (DOF) dynamic and kinematic models are constructed considering time-delay effects. A control scheme utilizing radial basis function (RBF) neural-network-(NN)-based adaptive sliding with planing force avoidance is proposed to simultaneously control the longitudinal stability and lateral motion of the supercavitating vehicle in the presence of external ocean-induced disturbances. The online estimation of nonlinear disturbances is conducted in real time by the designed NN and compensated for the dynamic control laws. The adaptive laws of the NN weights and control parameters are introduced to improve the performance of the NN. The least squares method is utilized to solve the actuator control efforts with rolling restriction in real-time online. Rigorous theoretical proofs based on the Lyapunov theory prove the globally asymptotic stability of the proposed controller. Finally, numerical simulations were performed to obtain maximum maneuverability and verify the effectiveness and robustness of the proposed control scheme.

Dynamic Output Feedback and Neural Network Control of a Non-Holonomic Mobile Robot.

This paper presents the design and synthesis of a dynamic output feedback neural network controller for a non-holonomic mobile robot. First, the dynamic model of a non-holonomic mobile robot is presented, in which these constraints are considered for the mathematical derivation of a feasible representation of this kind of robot. Then, two control strategies are provided based on kinematic control for this kind of robot. The first control strategy is based on driftless control; this means that considering that the velocity vector of the mobile robot is orthogonal to its restriction, a dynamic output feedback and neural network controller is designed so that the control action would be zero only when the velocity of the mobile robot is zero. The Lyapunov stability theorem is implemented in order to find a suitable control law. Then, another control strategy is designed for trajectory-tracking purposes, in which similar to the driftless controller, a kinematic control scheme is provided that is suitable to implement in more sophisticated hardware. In both control strategies, a dynamic control law is provided along with a feedforward neural network controller, so in this way, by the Lyapunov theory, the stability and convergence to the origin of the mobile robot position coordinates are ensured. Finally, two numerical experiments are presented in order to validate the theoretical results synthesized in this research study. Discussions and conclusions are provided in order to analyze the results found in this research study.

Gliding Vehicle Controller Based on Neural Network Compensating Dynamic Inversion Error

Aiming at the attitude control problem of the gliding vehicle with uncertainty and strong coupling, a dynamic inversion control method based on RBF neural network compensated inversion error is discussed. Firstly, based on the double time scale separation hypothesis, the controlled aircraft model is divided into a fast and slow state subsystem. Then the dynamic inversion control laws are designed for each of the two subsystems. The weight update rule of the RBF neural network is derived online based on the Lyapunov stability principle to compensate for the inversion error caused by the modeling error and uncertainty. The simulation verifies the effectiveness of the control law. The robustness of the control system after neural network compensation is significantly improved.

Output feedback control of uncertain Euler–Lagrange systems by internal model

In this paper, we investigate the trajectory tracking control problem of a class of uncertain Euler–Lagrange systems subject to disturbances. In sharp contrast to existing approaches where the position, the velocity, and the acceleration of the reference trajectory are assumed to be measurable, we propose a class of dynamic output feedback control laws which depends on the tracking error of the position and that of the velocity. Specifically, by characterizing the reference trajectory and the disturbances with an exosystem, we design an internal model to learn the desired feedforward input such that the reference trajectory can be tracked in spite of unknown system parameters and disturbances. The effectiveness of the proposed approach is illustrated by its application to trajectory tracking control of a three-link cylindrical robot arm.